Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913076194836480 |
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| author | López-Pastor, César Pedraza, Tatiana Rodríguez-López, Jesús |
| author_facet | López-Pastor, César Pedraza, Tatiana Rodríguez-López, Jesús |
| contents | We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also show that, by means of this isomorphism, the topology associated with a quasi-pseudometric modular coincides with that generated by its corresponding quantale enriched category.
Furthermore, we demonstrate that the class of quasi-pseudometrizable topological spaces coincides with the topological spaces whose topology is induced by a quasi-pseudometric modular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27588 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories López-Pastor, César Pedraza, Tatiana Rodríguez-López, Jesús Category Theory General Topology 46A80, 54E99, 18M05 We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also show that, by means of this isomorphism, the topology associated with a quasi-pseudometric modular coincides with that generated by its corresponding quantale enriched category. Furthermore, we demonstrate that the class of quasi-pseudometrizable topological spaces coincides with the topological spaces whose topology is induced by a quasi-pseudometric modular. |
| title | Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories |
| topic | Category Theory General Topology 46A80, 54E99, 18M05 |
| url | https://arxiv.org/abs/2604.27588 |